\({\cal CP}\)  violation in the interactions between the Higgs boson and the top quark can be probed experimentally within this framework using two different strategies: In a direct approach, a pure \({\cal CP}\) -odd observable is constructed, typically from angular distributions of Higgs boson production [1]}, [2]} or decay [3]}, [4]}, [5]}. Such a measurement can be used to constrain all models where both the \({\cal CP}\) -odd and the \({\cal CP}\) -even components of the Higgs boson couple with significant strength to the particle from which the \({\cal CP}\) -odd observable is measured. For the experimental establishment of \({\cal CP}\)  violation in the Higgs boson sector, the measurement of a \({\cal CP}\) -odd observable with a non-zero result would be crucial. For the Higgs–top-quark coupling, no experimental analysis of a pure \({\cal CP}\) -odd observable [6]}, [7]} exists yet. In an indirect approach, the model parameters are fitted to \({\cal CP}\) -even observables such as decay rates and kinematic distributions (e.g. \(p_T\)  spectra), and constraints on the \({\cal CP}\)  nature of the Higgs boson are derived indirectly from the constraints on the model parameters. This latter approach is the one followed in this paper. While the indirect approach is a very powerful test of possible deviations from the SM, in case a significant deviation is found it is not guaranteed that its origin can uniquely be associated with the presence of \({\cal CP}\) -violating effects. Thus, in order to determine the \({\cal CP}\)  nature of the Higgs sector, the two approaches are complementary.
